{"id":175,"date":"2016-03-04T11:15:02","date_gmt":"2016-03-04T16:15:02","guid":{"rendered":"https:\/\/adultnumeracyatterc.wordpress.com\/?p=175"},"modified":"2016-03-04T11:15:02","modified_gmt":"2016-03-04T16:15:02","slug":"the-right-formula","status":"publish","type":"post","link":"https:\/\/www.terc.edu\/adultnumeracycenter\/the-right-formula\/","title":{"rendered":"The \u201cRight\u201d Formula?"},"content":{"rendered":"

by Connie Rivera<\/p>\n

I was a participant in a training recently where we were given the tools to \u201cdiscover\u201d one of the not-as-common formulas provided on the Formula Sheet for the Hi-SET test. After some exploration experiences, we were asked to write an equation that showed the relationship between the variables that could be used to find the area of any such shape. Many of the other teachers already knew the formula and were able to link together the ideas to explain how to get the most common representation of the formula (the one on the Formula Sheet). Because I did not know the<\/em> formula, the formula I created represented what I saw as I worked through patterns and constants in an example problem. My version made me feel accomplished and like I had a deeper understanding. It made sense to me and I could explain how to get there, making a composite of more common shapes. However, when the others at my table saw such an unusual equation, the general reaction was, \u201cThat can\u2019t be right!\u201d My tablemates spent some time re-arranging my equation and learned that it did actually work. It sparked a conversation about the \u201cright formula\u201d and there was a sense at the table that I hadn\u2019t really gotten the answer right<\/em>.<\/p>\n

As someone who struggled through math the first time around, and who was told to follow a formula that I couldn\u2019t \u201csee,\u201d I now think, \u201cWhy?\u201d What do we accomplish by insisting that all students do things the same way? I think that permission to see math flexibly is part of what freed me from some of the anxiety that math still brings all these years into studying it. If one student sees the perimeter of a rectangle as l<\/em> + l<\/em> + w<\/em> + w<\/em>, another (L+W) + (L+W), and someone else sees 2x +2y, as long as they can explain the meaning, recognize it in other forms, and know how to use the formula to find perimeter or a side when the perimeter is known, does it really matter? When a student creates a formula, they \u201cown\u201d it and connect to it. It has meaning. To be honest, I still can\u2019t \u201csee\u201d the formula on the Hi-SET Formula Sheet and so I still can\u2019t tell you that formula without looking it up. It doesn\u2019t make sense to me that way. However, I can still re-create the formula I created and find the area of that shape even though the session was over a month ago. So, not only is this the way it made sense to me, but it was something I retained because I connected to it.<\/p>\n

When I attended college, I planned my schedule to avoid math. It wasn\u2019t until I was a GED Prep teacher that I started facing it again. Because I knew it was my weakness, I attended a math PD session and it ended up changing my life. It opened my eyes to the way it can feel to receive math instruction. I hope my engineer father never finds this blog, but I can tell you that being told tricks to memorize a formula that didn\u2019t make sense to me (like \u201cCornbread are round, pi R squared!\u201d) feels very different than being guided through a sequence of math experiences and being asked generative questions to draw a formula or a solution out of me. I do not feel the same sense of accomplishment and deepened understanding when using traditional formulas like those on the Formula Sheet to \u201cplug and chug\u201d \u2013 substituting numbers from a word problem into the formula without thinking.<\/p>\n

Have you ever noticed that many students who can use A = \u03c0r\u00b2 to tell you the area of a circle can\u2019t use the area to tell you the radius or diameter? It\u2019s not just that they don\u2019t know the steps to manipulate a formula and isolate a variable. It\u2019s more than that. They don\u2019t \u201csee\u201d the meaning of each variable and the relationship between those parts. I wonder what would happen if we started by leading students to discover pi as a relationship between two variables rather than thinking of it as just a number that never ends?<\/p>\n

==============================================================<\/p>\n

\"connieConnie Rivera teaches numeracy skills to adults of various skill levels, including court-involved youth and English Language Learners. She is also a math consultant, providing math strategies and support to programs implementing the College and Career Readiness (CCR) Standards for Adult Education in Connecticut and Massachusetts. As a consultant for the SABES numeracy team, Connie facilitates trainings and guides teachers in curriculum development. Connie is President-elect of the Adult Numeracy Network and a LINCS national trainer for math and numeracy.<\/em><\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

by Connie Rivera
\nI was a participant in a training recently where we were given the tools to \u201cdiscover\u201d one of the not-as-common formulas provided on the Formula Sheet for the Hi-SET test. After some exploration experiences, we were asked to write an equation that showed the relationship between the variables that could be used to find the area of any such shape. Many of the other teachers already knew the formula and were able to link together the ideas to explain how to get the most common representation of the formula (the one on the Formula Sheet).  » Read more<\/a><\/p>\n","protected":false},"author":31,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","footnotes":""},"categories":[1],"tags":[31,63,66],"class_list":["post-175","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-conceptual-understanding","tag-math-retention","tag-matth-formulas"],"acf":[],"cp_meta_data":{"_rest_api_published":["1"],"_rest_api_client_id":["-1"],"_publicize_job_id":["20432814925"]},"_links":{"self":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/posts\/175","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/users\/31"}],"replies":[{"embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/comments?post=175"}],"version-history":[{"count":0,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/posts\/175\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/media?parent=175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/categories?post=175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/tags?post=175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}